Please help me solve this problem and explain the steps

Answer:

[tex]\frac{dw}{dr} = \frac{8\cdot r}{4\cdot r^{2}-t^{2}+5\cdot s^{2}}[/tex], [tex]\frac{dw}{ds} = \frac{10\cdot s}{4\cdot r^{2}-t^{2}+5\cdot s^{2}}[/tex], [tex]\frac{dw}{dt} = -\frac{2\cdot t}{4\cdot r^{2}-t^{2}+5\cdot s^{2}}[/tex]

Step-by-step explanation:

We proceed to derive each expression by rule of chain. Let be [tex]w = \ln (x+2\cdot y + 3\cdot z)[/tex], [tex]x = r^{2}+t^{2}[/tex], [tex]y = s^{2}-t^{2}[/tex] and [tex]z = r^{2}+s^{2}[/tex]:

[tex]\frac{dw}{dr} = \frac{\frac{dx}{dr}+2\cdot \frac{dy}{dr} +3\cdot \frac{dz}{dr} }{x+2\cdot y + 3\cdot z}[/tex]

[tex]\frac{dx}{dr} = 2\cdot r[/tex]

[tex]\frac{dy}{dr} = 0[/tex]

[tex]\frac{dz}{dr} = 2\cdot r[/tex]

[tex]\frac{dw}{dr} = \frac{8\cdot r}{(r^{2}+t^{2})+2\cdot (s^{2}-t^{2})+3\cdot (r^{2}+s^{2})}[/tex]

[tex]\frac{dw}{dr} = \frac{8\cdot r}{4\cdot r^{2}-t^{2}+5\cdot s^{2}}[/tex] (1)

[tex]\frac{dw}{ds} = \frac{\frac{dx}{ds}+2\cdot \frac{dy}{ds} +3\cdot \frac{dz}{ds} }{x+2\cdot y + 3\cdot z}[/tex]

[tex]\frac{dx}{ds} = 0[/tex]

[tex]\frac{dy}{ds} = 2\cdot s[/tex]

[tex]\frac{dz}{ds} = 2\cdot s[/tex]

[tex]\frac{dw}{ds} = \frac{10\cdot s}{(r^{2}+t^{2})+2\cdot (s^{2}-t^{2})+3\cdot (r^{2}+s^{2})}[/tex]

[tex]\frac{dw}{ds} = \frac{10\cdot s}{4\cdot r^{2}-t^{2}+5\cdot s^{2}}[/tex] (2)

[tex]\frac{dw}{dt} = \frac{\frac{dx}{dt}+2\cdot \frac{dy}{dt} +3\cdot \frac{dz}{dt} }{x+2\cdot y + 3\cdot z}[/tex]

[tex]\frac{dx}{dt} = 2\cdot t[/tex]

[tex]\frac{dy}{dt} = -2\cdot t[/tex]

[tex]\frac{dz}{dt} = 0[/tex]

[tex]\frac{dw}{dt} = -\frac{2\cdot t}{(r^{2}+t^{2})+2\cdot (s^{2}-t^{2})+3\cdot (r^{2}+s^{2})}[/tex]

[tex]\frac{dw}{dt} = -\frac{2\cdot t}{4\cdot r^{2}-t^{2}+5\cdot s^{2}}[/tex] (3)

Answer:

Gddghdhdhdhy heifer here early enough h her y

Answer:

0

Step-by-step explanation:

the initial value is just the base line

Answer:

The answer is C. Right

Answer:

the nearest value is 1700

Answer:

-7

Step-by-step explanation:

Answer:

1/5, 1/6, 1/7 is expressions not greater than 1/4

Step-by-step explanation:

Answer:

A. The median of the data values is 16.

Step-by-step explanation:

Answer:

A - 16

Step-by-step explanation:

Answer:

The distance is 5 units

Step-by-step explanation:

Use the distance formula to find the distance.

Answer:

2,600.6

I think its 2,600.6 because 6% is 6 dollers I dont know if I am correct lol! but have a nice day! =)

Question for the Poster: Can I get brainliest,Thanks.Please type your questions with correct spelling so you can get your question answered to the best of everyone's ability

Answer:Maya reads 43 and 3/4 or 43.75 pages in 1 hour(or 44 pages per hour)

Answer:

Step-by-step explanation:

Square footage. ft². lock autosave. If you need to calculate the square footage of the floor's area, check out our square footage calculator.

Answer:

x=15

Step-by-step explanation:

If each of those expressions is the measure of each arc of the circle, when added together they should equal 360

8x-10+6x+10x+10=360

24x=360

x=15

Answer:

G is the same as the other one so it's also 129. Their angle relationship are verticle angles.

Answer:

15 students whose name begins with N

Step-by-step explanation:

This is not a valid representative sample.

Answer:

6/8>7/12

Step-by-step explanation:

6/8>7/12

36/48>28/48

I think

Answer:

x^2+3x−4

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

If evaluated this is the answer!

Answer:

48 yd²

Step-by-step explanation:

The shaded region is a trapezoid

Area of shaded region = area of the trapezoid

Area of trapezoid = ½(a + b)h

a = 6 yd

b = 10 yd

h = 15 - 9 = 6 yd

Area of trapezoid = ½(6 + 10)6

= ½(16)6

= 48 yd²

Area of the shaded region = 48 yd²

Answer: Y=83

Step-by-step explanation:

Answer:

y = 92

Step-by-step explanation:

plug in x = 27 into the equation y = 3x + 11,

y = 3(27) + 11

=> y = 81 + 11

=> y = 92

Answer:

8 mm

Step-by-step explanation:

Answer attached....

Hope it helps :)

Answer:

a = 8mm is the answer

Step-by-step explanation:

a = ?

b = 6mm

c = 10mm

By using the Pythagoras theorem,

a² + b² = c²

a² + 6² = 10²

a² + 36 = 100

a² = 100 - 36

a² = 64

a = 8

∴ a = 8mm is the length of the missing leg

Answer:

√2

Step-by-step explanation:

3x^2+4x-8+2x^2-4x-2

5X^2-10

5x^2=10

X^2=10/5

X^2=2

X=√2

Answer:

64/77

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation:

2/6*1/6= 2/12

When you simplify 2/12 you get 1/6

Answer:

120°

Shape Sides Each Angle

Hexagon    6              120°

Answer:

It's D

Step-by-step explanation:

Edge 2021

The complete step 3 in the proof is 2sin(x) {1+ cos(x)}.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

Given expression:

sin2(x) + 2sin(x)

This is the first step.

And the second step is given,

2sin(x)cos(x) + 2sin(x)

And to find the third step:

Simplify,

Factor out the common factor,

2sin(x) {1+ cos(x)}.

Therefore, the required step is 2sin(x) {1+ cos(x)}.

To learn more about the expression;

brainly.com/question/24242989  

#SPJ2

Answer:2

Step-by-step explanation:

Answer:

56sq. cm

Step-by-step explanation:

Area of a trapezoid = 1/2(a+b)h

a and b are the parallel sides

h is the height of the trapezoid

Find the f=diagram attached. from the diagram

a = 9cm

b = 5 + 9 + 5 = 19cm

h = 4cm

Substitute

Area of the trapezoid = 1/2 * (9+19)*4

Area of the trapezoid = 1/2 * 28 * 4

Area of the trapezoid = 28 * 2

Area of the trapezoid = 56sq. cm

Answer:

No

Step-by-step explanation:

To estimate population proportion from a sample, we must ensure that the sample data is random. Though a simple random sample of college students from a particular college was used as the sample data. However, selection of the college should have been randomized as well, a stratified random sample would have been a better sampling method whereby certain colleges are selected based on region or other criteria and then a random sample of it's statistics students selected. The sample proportion Obtian from a sample of this nature will be more representative of the population proportion of all college statistic student.